Starting with the work of Kraus et al,[1]} a strategy emerged for the emulation of topological effects from higher dimensions. It relies on aperiodicity, specifically, on the fact that any aperiodic pattern has an intrinsic degree of freedom, the phason, which, at least in principle, can be engineered, accessed and controlled experimentally.[2]}, [3]} The phason space augments the physical space and this opens a door to higher dimensional physics. Certainly, the experimental emulations of the 4D QHE were based on these principles.[4]}, [5]} Working with ultracold atoms, Lohse et al [4]} were able to map a cloud's center of mass as it navigated an aperiodically modulated potential and to demonstrate the quantization of the bulk topological invariant via a connection established in an earlier theoretical work.[7]} The bulk-boundary correspondence was not addressed in this study. Zilberberg et al[5]} emulated the 4D QHE with spatially modulated arrays of coupled optical wave guides and produced evidence of topological boundary modes. However, due to the specific physics involved, the analysis rested entirely on the spatial profile of the modes and their actual energies were not resolved. As such, no evidence of the hallmark Weyl singularity in the dispersion of the boundary modes was presented, predicted by the strong bulk-boundary correspondence of 4D QHE [9]}. Instead, other weaker forms of bulk-boundary correspondence were presented, such as the corner-to-corner pumping.
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